{"paper":{"title":"$L^p$-$L^q$ multipliers on locally compact groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.RT","authors_text":"Michael Ruzhansky, Rauan Akylzhanov","submitted_at":"2015-10-19T12:28:29Z","abstract_excerpt":"In this paper we discuss the $L^p$-$L^q$ boundedness of both spectral and Fourier multipliers on general locally compact separable unimodular groups $G$ for the range $1<p\\leq q<\\infty$. We prove a Lizorkin type multiplier theorem for $1<p\\leq q<\\infty$, and then refine it as a H\\\"ormander type multiplier theorem for $1<p\\leq 2\\leq q<\\infty$. In the process, we establish versions of Paley and Hausdorff-Young-Paley inequalities on general locally compact separable unimodular groups. As a consequence of the H\\\"ormander type multiplier theorem we derive a spectral multiplier theorem on general lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06321","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}